Question

Two rectangular matrices of order $n\times m$ and $m\times k$ are multiplied in the same order. The resulting matrix formed is a:

• A. Rectangular Matrix of order $n\times k$
• B. Square matrix of order $m$
• C. Square matrix of order $n$ if $n=k$
• D. Rectangular Matrix of order $k\times n$

Answer 1

Answer: (A), (C)

The correct options are
A Rectangular Matrix of order $n\times k$
C Square matrix of order $n$ if $n=k$

If there are $m$ rows and $n$ columns in the matrix, then the matrix is called $m\times n$ matrix.

A matrix having equal number of rows and columns is called square matrix.

So multiplying $2$ rectangular matrix of order $(n\times m)$ and $(m\times k)$ is a rectangular matrix of order $n\times k$ or it can also be a square matrix of order $n$ if $n=k$